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Quantum key-recovery attacks on FBC algorithm 基于FBC算法的量子密钥恢复攻击
IF 2.2 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2026-03-02 DOI: 10.1007/s11128-026-05098-0
Yan-Ying Zhu, Bin-Bin Cai, Fei Gao, Song Lin

With the advancement of quantum computing, symmetric cryptography faces new challenges from quantum attacks. These attacks are typically classified into two models: Q1 (classical queries) and Q2 (quantum superposition queries). In this context, we present a comprehensive security analysis of the FBC algorithm considering quantum adversaries with different query capabilities. In the Q2 model, we first design 4-round polynomial-time quantum distinguishers for FBC-F and FBC-KF structures, and then perform (r(r>6))-round quantum key-recovery attacks. Our attacks require (O(2^{(2n(r-6)+3n)/2})) quantum queries, reducing the time complexity by a factor of (2^{4.5n}) compared with quantum brute-force search, where n denotes the subkey length. Moreover, we give a new 6-round polynomial-time quantum distinguisher for FBC-FK structure. Based on this, we construct an (r(r>6))-round quantum key-recovery attack with complexity (O(2^{n(r-6)})). Considering an adversary with classical queries and quantum computing capabilities, we demonstrate low-data quantum key-recovery attacks on FBC-KF/FK structures in the Q1 model. These attacks require only a constant number of plaintext-ciphertext pairs, then use the Grover algorithm to search the intermediate states, thereby recovering all keys in (O(2^{n/2})) time.

随着量子计算的发展,对称密码学面临着来自量子攻击的新挑战。这些攻击通常分为两种模型:Q1(经典查询)和Q2(量子叠加查询)。在此背景下,我们对FBC算法进行了全面的安全性分析,考虑了具有不同查询能力的量子对手。在Q2模型中,我们首先针对FBC-F和FBC-KF结构设计了4轮多项式时间量子区分器,然后执行(r(r>6)) -round量子密钥恢复攻击。我们的攻击需要(O(2^{(2n(r-6)+3n)/2}))量子查询,与量子暴力搜索相比,将时间复杂度降低了(2^{4.5n}),其中n表示子密钥长度。此外,我们还给出了FBC-FK结构的一个新的6轮多项式时间量子区分符。在此基础上,我们构造了一个复杂度为(O(2^{n(r-6)}))的(r(r>6)) -round量子密钥恢复攻击。考虑到对手具有经典查询和量子计算能力,我们在Q1模型中演示了对FBC-KF/FK结构的低数据量子密钥恢复攻击。这些攻击只需要固定数量的明文-密文对,然后使用Grover算法搜索中间状态,从而在(O(2^{n/2}))时间内恢复所有密钥。
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引用次数: 0
Quantum neural networks for casting defect detection: a hybrid intelligence framework for smart manufacturing 用于铸造缺陷检测的量子神经网络:面向智能制造的混合智能框架
IF 2.2 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2026-02-26 DOI: 10.1007/s11128-026-05113-4
Nabhan Yousef, Chandrasinh Parmar, Amit Sata, Abhilash Edacherian

Defect detection in castings is essential for ensuring structural reliability in quality-critical industries. Traditional deep learning approaches face challenges such as high computational cost, susceptibility to noise, and overfitting when trained on limited datasets. To address these issues, we propose a hybrid quantum–classical framework for automated casting defect detection using quantum-inspired neural networks (QNNs). Here, “quantum-inspired” refers to algorithms based on principles of quantum walks and variational quantum circuits, implemented on classical simulation hardware. The model combines classical preprocessing with quantum variational layers to classify defects such as porosity, shrinkage, and micro-cracks from X-ray images. Experiments on the GDXray Castings dataset show that the eight-qubit QNN achieved 93.8% accuracy, 92.7% precision, 94.5% recall, and an F1-score of 93.6%, surpassing a baseline convolutional neural network. This work provides the first reported use of QNNs for casting inspection, offering a promising pathway toward robust and scalable non-destructive testing solutions in smart manufacturing.

在质量要求很高的行业中,铸件缺陷检测是保证铸件结构可靠性的关键。传统的深度学习方法面临着计算成本高、易受噪声影响以及在有限数据集上训练时过拟合等挑战。为了解决这些问题,我们提出了一个混合量子-经典框架,用于使用量子启发神经网络(QNNs)进行自动铸造缺陷检测。这里,“量子启发”是指基于量子行走和变分量子电路原理的算法,在经典仿真硬件上实现。该模型将经典预处理与量子变分层相结合,从x射线图像中对孔隙、收缩和微裂纹等缺陷进行分类。在GDXray casting数据集上的实验表明,8量子比特QNN的准确率为93.8%,精密度为92.7%,召回率为94.5%,f1分数为93.6%,超过了基线卷积神经网络。这项工作首次报道了qnn在铸件检测中的应用,为智能制造中鲁棒和可扩展的无损检测解决方案提供了一条有希望的途径。
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引用次数: 0
Non-convex optimization algorithm based on alternating quantum walk with potentials 基于位势交替量子行走的非凸优化算法
IF 2.2 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2026-02-26 DOI: 10.1007/s11128-026-05107-2
Dan Li, Guoliang Ju

This paper proposes a new model, alternating quantum walk with potentials (AQWP), designed to solve high-dimensional non-convex optimization problems. The method integrates problem-dependent potential-induced phase modulation into an alternating discrete-time quantum walk, enabling directional interference bias toward descent directions while preserving coherent quantum dynamics. A formal analysis of the algorithmic mechanism demonstrates that potential-induced phases generate constructive interference along descent paths and destructive interference elsewhere, with finite potential barriers traversable via quantum tunneling. Under mild regularity assumptions, this yields probabilistic concentration near low-energy regions instead of trapping at local minima. Computational complexity analysis of AQWP, accounting for classical preprocessing and quantum evolution, shows the overall cost scales polynomially with problem dimension and iteration count. To address parameter sensitivity, an online local estimation strategy for the phase normalization parameter is introduced, revealing a broad robustness interval that obviates global landscape scanning. Extensive numerical experiments on benchmark non-convex functions and binary classification neural networks confirm AQWP’s stability under random initialization and favorable scaling with input dimension and network capacity. Compared with classical baselines, AQWP consistently achieves faster convergence and better solution quality, establishing it as a scalable, robust quantum-inspired optimization paradigm for non-convex learning tasks.

本文提出了一种求解高维非凸优化问题的新模型——带势交替量子行走(AQWP)模型。该方法将问题相关的电位诱导相位调制集成到交替的离散时间量子行走中,在保持相干量子动力学的同时,实现了对下降方向的定向干涉偏置。对算法机制的形式化分析表明,势诱导相位沿下降路径产生建设性干涉,在其他地方产生破坏性干涉,通过量子隧道可穿越有限势垒。在温和的规则假设下,这产生了低能量区域附近的概率集中,而不是在局部最小值处捕获。考虑经典预处理和量子演化的AQWP计算复杂度分析,将总代价尺度与问题维数和迭代次数呈多项式关系。为了解决参数敏感性问题,引入了相位归一化参数的在线局部估计策略,揭示了广泛的鲁棒区间,从而避免了全局扫描。在基准非凸函数和二元分类神经网络上进行的大量数值实验证实了AQWP在随机初始化下的稳定性,以及随输入维数和网络容量的良好缩放。与经典基线相比,AQWP始终实现更快的收敛速度和更好的解质量,使其成为非凸学习任务的可扩展,鲁棒的量子启发优化范例。
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引用次数: 0
Computation of the smooth max-mutual information via semidefinite programming 基于半定规划的光滑最大互信息计算。
IF 2.2 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2026-02-25 DOI: 10.1007/s11128-026-05101-8
Christopher Popp, Tobias C. Sutter, Beatrix C. Hiesmayr

We present an iterative algorithm based on semidefinite programming (SDP) for computing the quantum smooth max-mutual information (I^varepsilon _{max }(rho _{AB})) of bipartite quantum states in any dimension. The algorithm is accurate if a rank condition for marginal states within the smoothing environment is satisfied and provides an upper bound otherwise. Central to our method is a novel SDP, for which we establish primal and dual formulations and prove strong duality. With the direct application of bounding the one-shot distillable key of a quantum state, this contribution extends SDP-based techniques in quantum information theory. Thereby it improves the capabilities to compute or estimate information measures with application to various quantum information processing tasks.

提出了一种基于半定规划(SDP)的迭代算法,用于计算任意维二部量子态的量子光滑最大互信息I max ε (ρ AB)。如果满足平滑环境中边缘状态的秩条件,则算法是准确的,否则提供上界。我们的方法的核心是一个新的SDP,我们建立了原始和对偶公式,并证明了强对偶性。通过直接应用限定量子态的一次性可蒸馏密钥,这一贡献扩展了量子信息理论中基于sdp的技术。从而通过应用于各种量子信息处理任务,提高了计算或估计信息测度的能力。
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引用次数: 0
Entanglement driven quantum cryptography for metropolitan optical networks 城域光网络的纠缠驱动量子密码
IF 2.2 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2026-02-25 DOI: 10.1007/s11128-026-05093-5
Abhishek Kumar, Abdul Khader Jilani Saudagar, Ankit Kumar

Quantum key distribution (QKD) entanglement-based solutions have become effective solutions for providing security to communications owing to the increased challenges posed by quantum computing. Entanglement-based QKD protocols are especially suitable for deployment over existing metropolitan optical fibre infrastructure, particularly those that provide device-independent security. Nonetheless, their implementation is strongly hindered by environmental noise, decoherence by optical fibres, and interference by co-existent classical data traffic. This research paper provides an overall experimental report on the noise resistance of entanglement-based QKD, in this case, the BBM92 protocol of a metropolitan fibre network. To solve practical problems, this study presents a hybrid model with three adaptive algorithms: the Adaptive entanglement purification protocol (AEPP), noise-resilient key reconciliation algorithm (NRKRA), and optimised privacy amplification technique (OPAT). The AEPP constantly checks the entanglement fidelity and enhances it through the purification of pairs of photons, depending on the real-time channel conditions. The NRKRA builds upon efficient key reconciliation by dynamically using error correction coded to optimise the observed quantum bit error rate (QBER). OPAT also enhances system security because it can handle privacy amplification based on the degree of information leakage. Experimental findings indicate that such a combined method is able to produce low QBER, high secret key rates with improved entanglement fidelity, even in the fibre links of up to 50 km length and in the presence of environmental experiments. This work has shown that an adaptable and resilient structure of this kind goes far beyond the conceptual frameworks of QKD modelling and real-world applications to provide insights on the necessary performance standards and to provide viable implementation guidelines to large-scale quantum cryptographic systems in the future.

由于量子计算带来的挑战越来越大,基于量子密钥分发(QKD)纠缠的解决方案已成为提供通信安全的有效解决方案。基于纠缠的QKD协议特别适合部署在现有的城域光纤基础设施上,特别是那些提供与设备无关的安全性的基础设施。然而,它们的实现受到环境噪声、光纤的退相干和共存的经典数据流量的干扰的严重阻碍。本文以城域光纤网络的BBM92协议为例,对基于纠缠的QKD的抗噪声性能进行了全面的实验研究。为了解决实际问题,本研究提出了一种混合模型,其中包含三种自适应算法:自适应纠缠净化协议(AEPP)、抗噪声密钥和解算法(NRKRA)和优化隐私放大技术(OPAT)。根据实时信道条件,AEPP不断检查纠缠保真度,并通过对光子的净化来提高纠缠保真度。NRKRA通过动态使用纠错编码来优化观察到的量子比特误码率(QBER),从而建立有效的密钥协调。OPAT还可以根据信息泄露的程度处理隐私放大,从而提高了系统的安全性。实验结果表明,即使在长达50公里的光纤链路和环境实验中,这种组合方法也能够产生低量子误码率、高密钥速率和改进的纠缠保真度。这项工作表明,这种适应性和弹性结构远远超出了QKD建模和现实世界应用的概念框架,为必要的性能标准提供了见解,并为未来的大规模量子密码系统提供了可行的实施指南。
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引用次数: 0
Entropy-based framework for quantum algorithm 1 robustness: discriminating noise channel impacts on 2 Shor’s period finding and establishing critical 3 performance thresholds 基于熵的量子算法框架1鲁棒性:区分噪声通道对2 Shor周期发现的影响以及建立关键的3性能阈值
IF 2.2 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2026-02-24 DOI: 10.1007/s11128-026-05094-4
Suresh Kumar Samarla, P. Maragathavalli, P. D. S. S. Lakshmi Kumari

Public-key cryptosystems such as RSA rely on the classical intractability of integer factorization, which is threatened by Shor’s quantum algorithm. While theoretically efficient, practical implementations face significant challenges due to noise in current quantum devices. This paper introduces an information-theoretic framework based on von Neumann entropy to analyze the robustness of Shor’s period-finding subroutine under various noise models. Through simulations of small moduli ((N=15,21)) under depolarizing, amplitude damping, and phase damping channels, this study demonstrates that entropy growth strongly correlates with success probability degradation, identify critical entropy thresholds marking the collapse of period finding, and report a robustness hierarchy, amplitude damping > phase damping > depolarizing noise. These findings provide hardware-agnostic insights for cryptanalytic security assessment and error mitigation strategies.

像RSA这样的公钥密码系统依赖于经典的整数分解的难解性,而这种难解性受到Shor量子算法的威胁。虽然理论上是有效的,但由于当前量子器件中的噪声,实际实现面临着重大挑战。本文引入了一个基于von Neumann熵的信息论框架,分析了Shor周期查找子程序在各种噪声模型下的鲁棒性。通过对去极化、振幅阻尼和相位阻尼通道下的小模量((N=15,21))的模拟,本研究证明了熵增长与成功概率退化密切相关,识别了标志着周期发现崩溃的临界熵阈值,并报告了鲁棒性层次,振幅阻尼&gt;相位阻尼&gt;去极化噪声。这些发现为密码分析安全评估和错误缓解策略提供了与硬件无关的见解。
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引用次数: 0
QryptGen+: a quantum GAN-based high-security image encryption key generator with enhanced chaotic modeling QryptGen+:基于量子gan的高安全性图像加密密钥生成器,具有增强的混沌建模
IF 2.2 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2026-02-23 DOI: 10.1007/s11128-026-05081-9
Gilsang Ahn, Seokhie Hong

Various approaches have been proposed to enable quantum generative adversarial networks (QGANs) to learn data distributions and generate images similar to original data. While QGANs are theoretically capable of modeling high-dimensional, complex distributions with fewer parameters and shorter training times than classical GANs, current hardware limitations hinder their performance. As a result, research has increasingly focused on identifying specific domains where QGANs can offer unique advantages. In our prior work, we proposed QryptGen, a PQWGAN-based framework for generating 28 (times ) 28 grayscale encryption key images from chaotic data. This demonstrated that QGANs can learn from visually indistinct, high-entropy distributions—beyond conventional datasets like MNIST—and produce image-based keys suitable for secure domains such as military communication, medical diagnostics, and cloud privacy systems. However, QryptGen’s use of row-wise patch stacking introduced inter-row correlations, reducing the randomness of the generated keys. Moreover, the PQWGAN loss function, optimized for structured data, was insufficient to fully capture the irregularity of chaotic distributions. To address these issues, we introduce QryptGen+, a redesigned framework that enhances randomness in key image generation. Key improvements include larger patch-wise generation to reduce structural bias, a strongly entangling quantum layer, a balanced training ratio between the generator and the critic, and a novel loss function that promotes anti-correlation and maximizes entropy. Through these refinements, QryptGen+ yields encryption keys with higher statistical security, reaffirming the potential of quantum machine learning for cryptographic applications.

为了使量子生成对抗网络(qgan)能够学习数据分布并生成与原始数据相似的图像,已经提出了各种方法。虽然理论上qgan能够用更少的参数和更短的训练时间来模拟高维、复杂的分布,但目前的硬件限制阻碍了它们的性能。因此,研究越来越集中于确定qgan可以提供独特优势的特定领域。在我们之前的工作中,我们提出了QryptGen,一个基于pqwgan的框架,用于从混沌数据中生成28张(times ) 28张灰度加密密钥图像。这表明,qgan可以从视觉上不清晰的高熵分布中学习——超越了mist等传统数据集——并产生适用于军事通信、医疗诊断和云隐私系统等安全领域的基于图像的密钥。然而,QryptGen使用逐行补丁堆叠引入了行间相关性,减少了生成密钥的随机性。此外,针对结构化数据优化的PQWGAN损失函数不足以充分捕捉混沌分布的不规则性。为了解决这些问题,我们引入了QryptGen+,这是一个重新设计的框架,增强了密钥映像生成的随机性。关键改进包括更大的补丁智能生成以减少结构偏差,强纠缠量子层,生成器和批评者之间的平衡训练比率,以及促进反相关和最大化熵的新型损失函数。通过这些改进,QryptGen+产生了具有更高统计安全性的加密密钥,重申了量子机器学习在密码学应用中的潜力。
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引用次数: 0
Quantum heat engine based on a three-spin-½ XX model with DM interaction and magnetic field 基于DM相互作用和磁场的三自旋1 / 2 XX模型的量子热机
IF 2.2 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2026-02-23 DOI: 10.1007/s11128-026-05109-0
Mohammad Reza Soltani, Maryam Mahmoodi, Fatemeh Khastehdel Fumani

This paper investigates the thermodynamic performance of a quantum heat engine (QHE) based on a three-spin-½ XX model in the presence of Dzyaloshinskii–Moriya (DM) interaction and an external magnetic field. By analyzing the system under varying DM coupling parameters and magnetic field strengths, we calculate the heat absorbed from the hot reservoir, heat released to the cold reservoir, net work output, and cycle efficiency. The results show that optimal engine performance, characterized by high positive work and efficiency, occurs when there is a significant asymmetry between the DM interaction strengths in the hot and cold stages of the cycle. In the absence of a magnetic field, a large D₁ and small D₂ enhance work extraction and efficiency. Introducing an external magnetic field modifies the energy spectrum through Zeeman splitting, leading to nontrivial behaviors such as isolated regions of positive work and reduced maximum efficiency. At strong field strengths, the interplay between DM interaction and the magnetic field becomes the dominant factor determining work output and efficiency. These findings highlight the sensitivity of spin-based quantum heat engines to interaction parameters and external control fields, offering insights into the design of efficient nanoscale thermal machines.

本文研究了在Dzyaloshinskii-Moriya (DM)相互作用和外加磁场作用下,基于三自旋-½XX模型的量子热机(QHE)的热力学性能。通过对系统在不同DM耦合参数和磁场强度下的分析,计算了系统从热储层吸收的热量、向冷储层释放的热量、净功输出和循环效率。结果表明,当循环的冷热阶段DM相互作用强度显著不对称时,以高正功和高效率为特征的最佳发动机性能才会出现。在没有磁场的情况下,大的D₁和小的D₂可以提高做功的提取率和效率。引入外部磁场通过塞曼分裂改变能谱,导致非平凡行为,如孤立的正功区域和降低的最大效率。在强场强下,DM相互作用与磁场的相互作用成为决定功输出和效率的主要因素。这些发现突出了基于自旋的量子热机对相互作用参数和外部控制场的敏感性,为高效纳米热机的设计提供了见解。
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引用次数: 0
An entropy-increasing circuit for quantum walking and its application in quantum encryption 量子行走增熵电路及其在量子加密中的应用
IF 2.2 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2026-02-21 DOI: 10.1007/s11128-026-05106-3
QingJi Zeng, JinQing Li, XiaoQiang Di

The rapid development of quantum computing poses a serious threat to traditional encryption techniques, especially in the field of image security, where traditional encryption schemes are difficult to resist quantum attacks. Therefore, research on quantum image encryption is crucial. In the research of quantum image encryption, the high randomness and high security of quantum keys have become the core elements to ensure system robustness. Therefore, in order to provide high-quality quantum keys, this study is inspired by low-dimensional quantum walk and proposes two quantum key generation schemes with high randomness: one is to construct a high-dimensional quantum walk paradigm using the physical properties of quantum walk; the second is to enhance the randomness of the basic quantum key by introducing an entropy-increasing circuit. On this basis, in order to verify the randomness and security of the key, a quantum walk-based scrambling algorithm and a shift-overlap XOR diffusion algorithm were designed, and corresponding quantum circuit implementations were provided. Finally, the proposed method was validated through security experiments. The experimental results show that the average entropy of the encrypted information is 7.9991, which is close to the ideal value, indicating that the key has good randomness. The robustness test results show that the ciphertext can effectively resist salt, pepper, and noise attacks. Meanwhile, the analysis of plaintext sensitivity shows that the NPCR value is 99.5431 and the UACI value is 33.5228, both of which meet the requirements of secure encryption systems.

量子计算的快速发展对传统的加密技术构成了严重的威胁,特别是在图像安全领域,传统的加密方案难以抵御量子攻击。因此,对量子图像加密的研究至关重要。在量子图像加密研究中,量子密钥的高随机性和高安全性成为保证系统鲁棒性的核心要素。因此,为了提供高质量的量子密钥,本研究受到低维量子行走的启发,提出了两种高随机性的量子密钥生成方案:一是利用量子行走的物理特性构建高维量子行走范式;二是通过引入熵增电路来增强基本量子密钥的随机性。在此基础上,为了验证密钥的随机性和安全性,设计了基于量子行走的置乱算法和移位重叠异或扩散算法,并给出了相应的量子电路实现。最后,通过安全实验对该方法进行了验证。实验结果表明,加密信息的平均熵为7.9991,接近理想值,表明该密钥具有良好的随机性。鲁棒性测试结果表明,该密文能够有效抵抗盐、胡椒和噪声攻击。同时,通过对明文灵敏度的分析,NPCR值为99.5431,UACI值为33.5228,均满足安全加密系统的要求。
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引用次数: 0
Simultaneous sharing of multiple l-level quantum states via compression and threshold encoding 通过压缩和阈值编码实现多个l级量子态的同时共享
IF 2.2 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Pub Date : 2026-02-20 DOI: 10.1007/s11128-026-05086-4
Hong Lai, Li Ren, Shengli Si, Josef Pieprzyk

To address the quantum resource bottleneck in conventional quantum secret sharing (QSS) and meet hierarchical security demands in multi-level quantum networks, this paper proposes a Hybrid Quantum State Sharing (HQSS) scheme that integrates quantum compression with classical threshold sharing. The protocol combines the Multi-scale Entanglement Renormalization Ansatz (MERA) for hierarchical quantum state compression with Shamir’s (tn) threshold scheme. Quantum states are compressed through disentanglement/isometry hierarchies, reducing l-level states to single qubits, while corresponding operation sequences are encoded as classical shares. The framework supports collaborative reconstruction requiring only one quantum participant and l classical participants. This work resolves scalability challenges in quantum networks through MERA-based compression and hybrid quantum–classical architecture. The scheme provides a practical solution for hierarchical quantum state sharing.

为了解决传统量子秘密共享(QSS)中的量子资源瓶颈,满足多层次量子网络的分层安全需求,提出了一种将量子压缩与经典阈值共享相结合的混合量子状态共享(HQSS)方案。该协议结合了用于分层量子态压缩的多尺度纠缠重整化Ansatz (MERA)和Shamir (t, n)阈值方案。量子态通过解纠缠/等距层次被压缩,将l级态减少到单个量子位,而相应的操作序列被编码为经典共享。该框架支持只需要一个量子参与者和1个经典参与者的协作重建。这项工作通过基于mera的压缩和混合量子经典架构解决了量子网络中的可扩展性挑战。该方案为分层量子态共享提供了一种实用的解决方案。
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引用次数: 0
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Quantum Information Processing
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